\documentclass[border=5pt]{standalone}
% \documentclass{article}
%\usepackage{math}
\usepackage{amsmath}

\begin{document}
  % \[
  %   y_m(t) = \frac{\displaystyle\sum_{n-1}^{N}{W_{nm}\vec{x}(t)}}{\sqrt{\displaystyle\sum_{n=1}^{N}{W_{nm}^2}}} = \frac{\vec{w}_m^T}{\left\|{\vec{w}_m}\right\|}\vec{x}(t)
  % \]
  $y_m(t) = \frac{\displaystyle\sum_{n-1}^{N}{W_{nm}\vec{x}(t)}}{\sqrt{\displaystyle\sum_{n=1}^{N}{W_{nm}^2}}} = \frac{\vec{w}_m^T}{\left\|{\vec{w}_m}\right\|}\vec{x}(t)$
%   $$
% a_1
%   $$
\end{document}

